This is a shame, that Andrew still hasn't been found and his case appears to be getting so little media attention now.
Two things struck me straight away - he insisted on buying a single ticket so it looks like he wanted people to know he wasn't coming back. Ominously, people about to harm themselves often leave no note and don't appear obviously depressed beforehand. But they do sometimes leave a tiny hint, and a one way ticket might qualify.
The other thing though, is that he headed to London. That's not exactly a likely suicide destination, apart from people who want to jump under trains. I don't think Andrew could have been heading to Chislehurst or Sidcup to the relatives; he'd have needed to get the Underground to London Bridge to make the connection, so I don't see why he would have walked out of King's Cross Mainline. Getting a cab there is so unlikely, I just can't believe he would have done that.
As Andrew was mathematically inclined, I'm guessing he liked maps too? (I have one like this at home!). The London tube map is particularly charming, lots of copies are free and so I think Andrew would have known exactly which tube he needed to get to reach wherever he was going.
Myself, I think he turned right towards the taxis not because he was heading for a taxi, but because he was heading for the road behind them (York Road??) beside St Pancras. Towards Camden Market, the goth/metal Mecca, for all goths who don't live in London (I think the London goths hang out elsewhere).
London is also interesting because it is the central connection point to almost every other destination in the UK, and mainland Europe. So if you wanted to hide your ultimate destination, it's an excellent place to do it.
I wonder if police have managed to obtain a DNA sample for Andrew (this is not something done routinely by UK police for missing persons)? And if a computer forensic expert has checked the family computer out? I'm not casting aspersions on the family here - I mean in case Andrew was using it in secret and deleted everything before he left.
I hope he is found soon. It is hard to see how a boy so young looking could survive on his own, but I am not convinced this young man (now) is deceased, myself.